The undergraduate Mathematics Colloquium (aka Math Table) sponsored by the
Mathematics Department, meets most Tuesday nights at 5:30 in Mather House
Private Dining Rooms A & B. Its purpose is to expose students to diverse
topics of pure and applied mathematics, to suggest potential Senior Thesis
topics. Speakers include faculty, guest speakers, graduate students and
undergraduate students. All students, irrespective of their mathematical
backgrounds, are strongly encouraged to attend and/or to give talks.
The two best undergraduate talks at the colloquium each year will win the
Rogers Prize.
For more information on the Mathtable, please contact
Noam Elkies (elkies@math.harvard.edu).

Next Mathtable

12/06/2016

Putnam Postmortem, by Noam Elkies, Harvard University

Click on the large icon to see all mini posters.

Solution outlines and/or mathematical context will
be given for some of the problems from last Saturday's
Putnam exam, likely starting with B1, B6, and A6.

Fall 2016

12/06/2016

Putnam Postmortem, by Noam Elkies, Harvard University

11/29/2016

Understanding Inequality: A Kinetic Model of Wealth, by Marek Johnson, Undergraduate at Tufts University

11/15/2016

A look at the Mercator Projection, by Carlos Albors-Riera, Harvard Undergraduate

Please congratulate the recipients of the Department's undergraduate
prizes and awards this year.
The Mumford Prize is awarded in 2013 to Eric Larson
The Wister Prize is awarded in 2013 to Tony Feng
The Herb Alexander Award is given this year to Ben Adlam
Two of our graduating seniors won 'Hoopes' Prizes for their theses this
year: please congratulate
Christian Anderson and Ashok Cutkosky.
The Rogers prize is award to Lucia Mocz, Akhil Mathew and
Dmitri Gekhtman. The Friends prize want to
Eric Larson. Tony Feng was the runner up.

Spring 2013

4/23/13

Modular Forms in String Theory, by Murad Alim , Harvard University

4/16/13

What is the Birch and Swinnerton-Dyer Conjecture?, by Lucia Mocz, Harvard Undergraduates

4/09/13

Who wants to be a Math concentrator?, by Zachary Abel,Tony Liu,Lucia Mocz,Robert Nishihara,John Sheridan,Caitlin Stanton, Harvard Alumni or Harvard Undergraduates

4/02/13

The Unique Games Conjecture and Hardness of Approximation , by Elena-Madalina Persu, Harvard Undergraduate

3/26/13

The sine integral Int(sin(x)/x,x,0,INFTY)=Pi/2 by elementary calculus, by Noam Elkies, Harvard University

Please congratulate the recipients of the Department's undergraduate
prizes and awards this year.

David Mumford Undergraduate Mathematics Prize

From the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M.
1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate
Mathematics Prize, to be given annually to the most promising senior
concentrator in mathematics, provided such concentrator is outstanding.
The David Mumford Undergraduate Mathematics Prize is awarded in 2011 to Arnav Tripathy.

Winster Prize

From the gift of Susan Alexander, the Herb Alexander Award recognizes
each year one of our outstanding undergraduates, and provides money to
be used for research and travel

The Wister Prize is awarded in 2011 to Sherry Gong.

Herb Alexander Award

From the gift of Susan Alexander, the Herb Alexander Award recognizes
each year one of our outstanding undergraduates, and provides money to
be used for research and travel.
The Herb Alexander Award is given this year to Jonathan Wang.

Robert Fletcher Rogers Prizes

From the income of the gift in 1921 of the late Robert Fletcher
Rogers, A.B. 1886, there have been established a first prize and second
prize to be awarded annually to the College students who present the
best talks before the Mathematics Table during an academic year.
The Rogers Prizes are awarded this year as follows:

First prize: Adrian Sanborn, for his talk Scaling Dimensions with Fractal Curves

Second prize: to be divided equally between Eric Larson for his talk
"An Inequality Involving the Perimeter and Curvature of Plane Curve", and
Akhil Mathew for his talk "Translation-Invariant Binary Representations".

Hoopes Prize

Michael Viscardi has been awarded the Hoopes' Prize this year, for his
senior thesis "Alternative compactifications of the moduli space of genus on maps."
Hoopes' Prizes were also won by two of our joint concentrators: Andrei
Cristea (Economics and Math), and Chrisopher Lim (Music and Math).

Photos of the mathtable of September 7, 2010. Shing-Tung Yau gives a talk on the maximum principle.
[See larger panorama photo].

Please congratulate the recipients of the Department's undergraduate
prizes and awards this year.

David Mumford Undergraduate Mathematics Prize

From the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M.
1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate
Mathematics Prize, to be given annually to the most promising senior
concentrator in mathematics, provided such concentrator is outstanding.
The Mumford Prize is awarded to Michael Viscardi.

Herb Alexander Award

From the gift of Susan Alexander, the Herb Alexander Award recognizes
each year one of our outstanding undergraduates, and provides money to
be used for research and travel.
The Herb Alexander Award is given this year to Zachary Abel.

Robert Fletcher Rogers Prizes

From the income of the gift in 1921 of the late Robert Fletcher
Rogers, A.B. 1886, there have been established a first prize and second
prize to be awarded annually to the College students who present the
best talks before the Mathematics Table during an academic year.
The two prizes are awarded equally this year to:

Hoopes Prize

Michael Viscardi has been awarded the Hoopes' Prize this year, for his
senior thesis "Alternative compactifications of the moduli space of genus on maps."
Hoopes' Prizes were also won by two of our joint concentrators: Andrei
Cristea (Economics and Math), and Chrisopher Lim (Music and Math).

Please congratulate the recipients of the Department's undergraduate
prizes and awards this year.

David Mumford Undergraduate Mathematics Prize

From the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M.
1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate
Mathematics Prize, to be given annually to the most promising senior
concentrator in mathematics, provided such concentrator is outstanding.
The Mumford Prize is awarded in 2009 jointly to John Lesieutre
and Shrenik Shah.

Wister Prize

From a bequest of Charles J. Wister, a prize is awarded in alternate
years to the Senior concentrating in Mathematics or Music who has the
highest record in his/her field of concentration. In 2008-09 the prize
is open to concentrators in Mathematics, in 2009-10 to concentrators in
Music.
The Wister Prize is awarded to Samuel Lichtenstein.

Herb Alexander Award

From the gift of Susan Alexander, the Herb Alexander Award recognizes
each year one of our outstanding undergraduates, and provides money to
be used for research and travel.
The Herb Alexander Award is given this year to Nike Sun.

Robert Fletcher Rogers Prizes

From the income of the gift in 1921 of the late Robert Fletcher
Rogers, A.B. 1886, there have been established a first prize and second
prize to be awarded annually to the College students who present the
best talks before the Mathematics Table during an academic year.
First Prize: Zachary Abel for his talk "Hinged dissections exist".
Second Prize: Laura Starkston, for her talk "Khovanov homology".

Please join me in congratulating the recipients of the Department's
undergraduate prizes and awards this year. br>

David Mumford Undergraduate Mathematics Prize

The Mumford prize is awarded to Dustin Clausen.
From the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M.
1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate
Mathematics Prize, to be given annually to the most promising senior
concentrator in mathematics, provided such concentrator is outstanding.

The Herb Alexander Award

The Herb Alexander Award is given this year to Elena Yudovina.
From the gift of Susan Alexander, the Herb Alexander Award recognizes
each year one of our outstanding undergraduates, and provides money to
be used for research and travel to mathematics conferences.

The Robert Fletcher Rogers Prizes:

First Prize: Scott Kominers, for his talk
"C=15".
Second Prize: Christian Zamora Jaen, for his talk
"Fermat's Last Theorem".
From the income of the gift in 1921 of the late Robert Fletcher
Rogers, A.B. 1886, there have been established a first prize and second
prize to be awarded annually to the College students who present the
best talks before the Mathematics Table during an academic year.

Hoopes Prizes

Dustin Clausen and Alison Miller were recipients of the Hoopes
Prizes this year, for their outstanding senior theses.
Congratulations again to all! br>
Peter Kronheimer, Director of Undergraduate Studies, Department of Mathematics

The Fraisse Construction and its Descendants, by Rehana Patel, Harvard University

3/14/08

Pi-day 2008, by Pi, Mathematical constant

3/4/08

Color by Numbers, by Daniel Litt, Harvard Undergraduate

2/26/08

Probabilistic Group Theory, by Bret Benesh, Harvard University

2/5/08

Curves, Cryptography and Primes of the Form x2 + D y2, by Juliana Belding , University of Maryland

Gabor Domokos visits Harvard on April 15'th 2008 and demonstrates the gomboc.
His mathtable talk was a big success.

The Gomboc was created
by Gabor Domokos and Peter Varkonyi, Budapest University of Technology and Economics.
The 'Gomboc' became very popular.
The website attracts hundreds of thousand of visitors (mostly
non-mathematicians) from over hundred countries.
References:

Abstract: The weeble (also called the 'Comeback Kid') is the favorite
of many children: whenever knocked over, it always returns to the same
(stable) equilibrium position. This toy is, of course, not homogenous,
spontaneous self-righting is guaranteed by the weight at the bottom. We
may also observe that most weebles have only one unstable balance point,
at the top.
When we look at homogeneous objects, the problem becomes less trivial. In
two dimensions, it is relatively easy to prove that each homogeneous,
convex slab has at least two stable (S=2) and two unstable (U=2)
equilibria when rolling under gravity on a horizontal surface, i.e.
homogeneous 2D weebles do not exist.
One can imagine several three dimensional generalizations to this
statement: a) S>1 b) U>1 c) S+U>2 While a) and b) can be shown to be
false, c) posed a considerable puzzle for many years. Finally, in 1995,
V.I. Arnold conjectured that c) is NOT true either, in other words,
convex, homogeneous solids with just one stable and one unstable point
of equilibrium (also called mono- monostatic) may exist. These are
'special weebles' which share the number and type of equilibria of the
toy, however, no weight is added.
Not only did his conjecture turn out to be true, the newly discovered
objects show various interesting features. Our goal is to give an
overview of these findings with emphasis on a qualitative approach based
on dynamical systems theory, as well as to present some new results. We
will point out that mono-monostatic bodies are neither flat, nor thin,
they are not similar to typical objects with more equilibria and they
are hard to approximate by polyhedra. Despite these "negative" traits,
there seems to be strong indication that these forms appear in Nature
due to their special mechanical properties.
These new forms, called 'Gomboc' became very popular on the internet,
the website attracting hundreds of thousand of visitors (mostly
non-mathematicians) from over hundred countries.

Fall 2007

12/11/07

Integers and Sequences, by Tanya Khovanova, Lead Analyst at BAE Systems

Please join me in congratulating the recipients of the Department's
undergraduate prizes and awards this year.

David Mumford Undergraduate Mathematics Prize

The Mumford prize is awarded to Kaloyan Slavov.
From the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M.
1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate
Mathematics Prize, to be given annually to the most promising senior
concentrator in mathematics, provided such concentrator is outstanding.

The Wister Prize

The Wister Prize is awarded to Anatoly Preygel.
From a bequest of Charles J. Wister, a prize is awarded in alternate
years to the Senior concentrating in Mathematics or Music who has the
highest record in his/her field of concentration. In 2006-07 the prize
is open to concentrators in Mathematics, in 2007-08 to concentrators in
Music.

The Herb Alexander Award

The Herb Alexander Award is given this year to Igor Rapinchuk.
From the gift of Susan Alexander, the Herb Alexander Award recognizes
each year one of our outstanding undergraduates, and provides money to
be used for research and travel to mathematics conferences.

The Robert Fletcher Rogers Prizes:

First Prize: Robin Walters, for his talk
"Generalizations of the Hexagonal Honeycomb Theorem".
Second Prize: Gerardo Con Diaz, for his talk
"Cutting and Pasting Doughnuts: Three Ways of Constructing Lens Spaces".
Honorable Mention: Alison Miller, for her talk "Exp(pi*Sqrt(163)) and Friends".
From the income of the gift in 1921 of the late Robert Fletcher
Rogers, A.B. 1886, there have been established a first prize and second
prize to be awarded annually to the College students who present the
best talks before the Mathematics Table during an academic year.

Hoopes Prizes

Mark Lipson and Kaloyan Slavov were recipients of the Hoopes
Prizes this year, for their outstanding senior theses. The Hoopes Prize
committee awarded Goutham Seshadri an honorable mention.

This year, the Mumford Prize will be split between
Stefan Patrikis, and Nikita Rozenblyum.

"From the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M.
1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate
Mathematics Prize, to be given annually to the most promising senior
concentrator in mathematics, provided such concentrator is
outstanding."

The Herb Alexander Award is given this year to
Sheel Ganatra.

"From the gift of Susan Alexander, the Herb Alexander Award recognizes
each year one of our outstanding undergraduates, and provides money to
be used for research and travel to mathematics conferences."

"From the income of the gift in 1921 of the late Robert Fletcher
Rogers, A.B. 1886, there have been established a first prize and
second prize to be awarded annually to the College students who
present the best talks before the Mathematics Table during an academic
year."

In addition Stefan Patrikis and Gregory Valliant were
recipients of Hoopes Prizes this year,
for their outstanding senior theses.

Congratulations to the winners of the prizes for undergraduates 2004-2005:

1. DAVID MUMFORD PRIZE will go to Gabriel Carroll and Ian Le

DAVID B. MUMFORD UNDEGRADUATE MATHEMATICS PRIZE
From the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M.
1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate
Mathematics Prize, to be given annually to the most promising senior
concentrator in mathematics, provided such concentrator is
outstanding.

2. ROBERT FLETCHER ROGERS PRIZES for 2004-2005:
First prize: Ronen Mukamel for his talk on
"Four Things You Can Do in the Hyperbolic Plane that Your Parents Couldn't in the Euclidean"
Two Second Prizes will go to:
Mike Hamburg for his talk on
"Compass and Straightedge Constructions for Projectile and Orbital Motion"Adam Levine for his talk on "Word-Hyperbolic Coxeter Groups"

ROBERT FLETCHER ROGERS PRIZE.
From the income of the gift in 1921 of the late Robert Fletcher Rogers,
A.B. 1886, there have been established a first prize and second prize
to be awarded annually to the College students who present the best
talks before the Mathematics Table during an academic year. In making
the awards, emphasis will be laid primarily on the excellence of the
oral presentation. It is not essential that the material presented be
original, but mastery of the subject and adaptation of the presentation
will be regarded as important. The prizes will be awarded by the
Department of Mathematics on the recommendation of the Mathematics
Table. For further information, please contact the Mathematics
Department.

3. The WISTER PRIZE will go to Andrei Jorza

WISTER PRIZE. From a bequest of Charles J. Wister, a prize is awarded
in alternate years to the senior concentrating in Mathematics or Music who has the
highest record in his/her field of concentration. In 2004-05 the prize
is open to concentrators in Mathematics, in 2005-06 to concentrators in
Music.

Spring 2005

5/10/05

Four things you can do in the Hyperbolic plane that your parents couldn't in the Euclidean, by Ronen Mukamel, Harvard Undergraduate

5/3/05

A Modular Proof of the Class Number One Problem, by Tseno Tselkov, Harvard Undergraduate

Tutorials, by Additive Number Theory and Algebraic Surfaces and Complex Manifolds of Higher Dimension, Michael Schein and Sabin Cautis

Congratulations to the winners of the Math Prizes 2003-2004:
1. DAVID MUMFORD PRIZE goes to Dimitar Jetchev
2. ROBERT FLETCHER ROGERS PRIZES for 2003-2004:
Corina Patrascu - the First Prize for a talk on
"Computing order statistics in the Farey sequence"
Jonathan Bloom - the Second Prize for a talk on
"The Local Structure of Smooth Maps of Manifolds"

Spring 2004

4/27/04

The Local Structure of Smooth Maps of Manifolds, by Jonathan Bloom, Harvard Undergraduate

DAVID B. MUMFORD UNDERGRADUATE MATHEMATICS PRIZE
From the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M.
1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate
Mathematics Prize, to be given annually to the most promising senior
concentrator in mathematics, provided such concentrator is outstanding.)

WISTER PRIZE
From a bequest of Charles J. Wister, a prize is awarded in alternate years
to the Senior concentrating in Mathematics or Music who has the highest
record in his/her field of concentration. In 2001-2002 the prize is open to
concentrators in Music, in 2002-03 to concentrators in Mathematics. Further
information may be obtained from the Departments of Mathematics and Music.)

ROBERT FLETCHER ROGERS PRIZE
From the income of the gift in 1921 of the late Robert Fletcher Rogers,
A.B. 1886, there have been established a first prize and second prize to be
awarded annually to the College students who present the best talks before
the Mathematics Table during an academic year. In making the awards,
emphasis will be laid primarily on the excellence of the oral presentation.
It is not essential that the material presented be original, but mastery of
the subject and adaptation of the presentation will be regarded as
important. The prizes will be awarded by the Department of Mathematics on
the recommendation of the Mathematics Table.